Displaying similar documents to “On the convergence of difference schemes for classical and weak solutions of the Dirichlet problem”

Penalization of Dirichlet optimal control problems

Eduardo Casas, Mariano Mateos, Jean-Pierre Raymond (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.

On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

Ta Van Dinh (1987)

Aplikace matematiky

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The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an n -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an ( n -dimensional) rectangular grid in the directions of the...